The correlation energy per electron in the high-density uniform electron gas can be written as $E_{\mathrm{c}}(r_s,\zeta )={\lambda }_0(\zeta )\ln r_s+{\varepsilon }_0(\zeta )+{\lambda }_1(\zeta )r_s\ln r_s+O(r_s)$, where $r_s$ is the Seitz radius and $\zeta$ is the relative spin polarization. We derive an expression for ${\lambda }_1(\zeta )$ that is exact for any $\zeta$, including the paramagnetic and ferromagnetic limits, ${\lambda }_1(0)$ and ${\lambda }_1(1)$, and discover that the previously published ${\lambda }_1(1)$ value is incorrect. We trace this error to an integration and limit that do not commute. The spin resolution of ${\lambda }_1(\zeta )$ into contributions of electron pairs is also derived.

• Received 17 May 2011

DOI:https://doi.org/10.1103/PhysRevB.84.033103